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Yes, Erick! Now the command prompt doesn't show any of them anymore.
I'll make a simpler test setup just with the pivot aplication and link in another blender file to see if it's a bug, or I'm doing something wrong.

But it's not a problem: It's the way a pivot has to work.
The weird behavior is due to the fact that I have previously rotated the main bone of the rig 90º in the Z axis, in the linked scene.
So then every transformation I do in the bone show me the final position of the bone considering it was rotated around the Pivot object.

Now I have this animation workflow, to animate a walk-cycle of the book around each of its corners:

Position the Pivot object (keyframe it);

Keyframe the transforms of the rig/bone;

Go to next frame to be keyed;

Rotate the rig/bone (keyframe it);

Set cursor position to the current position of the bone (to record it);

Move Pivot object to new position (and keyframe it);

Fix the position of the bone based on the previous position, recorded in cursor (and keyframe it);

Contunue the cycle from step 3...

WHAT CHANGED: now I have to store the bone position in the cursor and restore it's Loc after I have moved the Pivot.

RESULT:

If any of you guys know any other solution for this walkcycle based on Pivots, please share with us!

Another way you can do this is to put a bone in your armature, not parented to anything. Then move this bone to where you want to pivot. Then put a child of constraint on the bone you want to move, ie root, and rotate the bone. This will rotate the whole character on that bone. You can then use the influence to turn it on or off and move it again to another location. The bone will allow you to use it in linked files on your proxy armature and you can also keyframe it in your actions.

It's amazing how many ways you can achieve desired results in Blender!

Another way you can do this is to put a bone in your armature, not parented to anything. Then move this bone to where you want to pivot. Then put a child of constraint on the bone you want to move, ie root, and rotate the bone. This will rotate the whole character on that bone. You can then use the influence to turn it on or off and move it again to another location. The bone will allow you to use it in linked files on your proxy armature and you can also keyframe it in your actions.